Question: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 5x + 1$ and $ KL = 7x - 3$ Find $JL$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {5x + 1} = {7x - 3}$ Solve for $x$ $ -2x = -4$ $ x = 2$ Substitute $2$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 5({2}) + 1$ $ KL = 7({2}) - 3$ $ JK = 10 + 1$ $ KL = 14 - 3$ $ JK = 11$ $ KL = 11$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {11} + {11}$ $ JL = 22$